Extended Discrete Element Method for subject specific modelling and analysis of the ankle joint contact mechanics

Osteoporosis related bone fractures and osteoarthritis affect the lifes of millions of people in the world and constitute a significant burden on the healthcare systems of several countries. It is believed that mechanical actors such as excessive joint loading during daily activities might play a role in their onset. Predictive methods based on computational modelling could identify the early development of such diseases and, among these techniques, the multiscale modelling approach shows promising potential in view of its capability to describe the musculoskeletal (MSK) system across different spatial and temporal levels. The development of a multiscale model of the MSK system, however, poses great computational challenges and requires the determination of multiscale links such as the joint contact pressure, which is typically predicted by means of computationally expensive methods such as the finite element method. An accurate low cost alternative is represented by the discrete element method (DEM), a computational method in which a spring mattress is used to describe the contact interactions within the joints. The method, however, has been developed for static cases and does not offer the possibility of tracking the physiological motion of the contacting bones over time. Furthermore, time dependent properties such as viscoelasticity are often neglected within these frameworks. This thesis aims at extending the discrete element method (EDEM) to track the bone motion and include the viscoelastic phenomena. The methodology is used, in conjunction with subject specific MSK models, for the development of subject specific ankle models to compute the contact pressure during gait. Evaluation of EDEM and DEM outputs found that not considering the physiological displacement of the talus causes an underestimation of the joint pressure distribution, while the peak values remain substantially unaffected. Comparison against experimental pressure data shows that EDEM can identify the patterns of pressure in cadaveric ankle specimens. Finally, the viscoelastic formulation of EDEM proved successful in describing the typical creep behaviour of articular cartilage.